Manifestly Gauge-Invariant Cosmological Perturbation Theory from Full Loop Quantum Gravity

Abstract

We apply the full theory of Loop Quantum Gravity (LQG) to cosmology and present a top-down derivation of gauge-invariant cosmological perturbation theory from quantum gravity. The derivation employs the reduced phase space formulation of LQG and the new discrete path integral formulation defined in arXiv:1910.03763. We demonstrate that in the semiclassical approximation and continuum limit, the result coincides with the existing formulation of gauge-invariant cosmological perturbation theory in e.g. arXiv:0711.0117. Time evolution of cosmological perturbations is computed numerically from the new cosmological perturbation theory of LQG, and various power spectrums are studied for scalar mode and tensor mode perturbations. Comparing these power spectrums with predictions from the classical theory demonstrate corrections in the ultra-long wavelength regime. These corrections are results from the lattice discretization in LQG. In addition, tensor mode perturbations at late time demonstrate the emergence of spin-2 gravitons as low energy excitations from LQG. The graviton has a modified dispersion relation and reduces to the standard graviton in the long wavelength limit.

arXiv comment26 pages, 16 figures. ILQGS talk: http://relativity.phys.lsu.edu/ilqgs/han041420.mp4. Mathematica files can be downloaded from https://github.com/LQG-Florida-Atlantic-University/cos_pert

References in corpus (29)

• Background Independent Quantum Gravity: A Status Report
• Quantum Nature of the Big Bang: Improved dynamics
• Absence of Singularity in Loop Quantum Cosmology
• Dust as a Standard of Space and Time in Canonical Quantum Gravity
• Fundamental Structure of Loop Quantum Gravity
• Gauge Field Theory Coherent States (GCS) : I. General Properties
• Anomaly-free scalar perturbations with holonomy corrections in loop quantum cosmology
• Gauge Field Theory Coherent States (GCS) : II. Peakedness Properties
• Algebraic Quantum Gravity (AQG) IV. Reduced Phase Space Quantisation of Loop Quantum Gravity
• Scalar Material Reference Systems and Loop Quantum Gravity
• Gauge Field Theory Coherent States (GCS) : III. Ehrenfest Theorems
• Gauge invariant cosmological perturbation equations with corrections from loop quantum gravity
• Gauge-Invariant Perturbations in Hybrid Quantum Cosmology
• Inflation in loop quantum cosmology: Dynamics and spectrum of gravitational waves
• Manifestly Gauge-Invariant General Relativistic Perturbation Theory: I. Foundations
• Alleviating the Tension in the Cosmic Microwave Background using Planck-Scale Physics
• Algebraic Quantum Gravity (AQG) III. Semiclassical Perturbation Theory
• Manifestly Gauge-Invariant General Relativistic Perturbation Theory: II. FRW Background and First Order
• Effective Dynamics from Coherent State Path Integral of Full Loop Quantum Gravity
• Anomaly-free vector perturbations with holonomy corrections in loop quantum cosmology
• Primordial power spectrum from the dressed metric approach in loop cosmologies
• Loop Quantum Cosmology: A brief review
• Hybrid Models in Loop Quantum Cosmology
• Improved ($\bar{\mu }$-Scheme) Effective Dynamics of Full Loop Quantum Gravity
• Phenomenology with fluctuating quantum geometries in loop quantum cosmology
• Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity
• Mukhanov-Sasaki equation in manifestly gauge-invariant linearized cosmological perturbation theory with dust reference fields
• Emergent 4-dimensional linearized gravity from spin foam model
• Modifications to Gravitational Wave Equation from Canonical Quantum Gravity

Cited by in corpus (10)

• Improved Effective Dynamics of Loop-Quantum-Gravity Black Hole and Nariai Limit
• Phenomenological implications of modified loop cosmologies: an overview
• States of Low Energy in bouncing inflationary scenarios in Loop Quantum Cosmology
• First-Order Quantum Correction in Coherent State Expectation Value of Loop-Quantum-Gravity Hamiltonian
• Loop Quantum Gravity on Dynamical Lattice and Improved Cosmological Effective Dynamics with Inflaton
• Loop quantum cosmology: relation between theory and observations
• Relating dust reference models to conventional systems in manifestly gauge invariant perturbation theory
• Scalar Quasi-Normal Modes of a Loop Quantum Black Hole
• Friedmann equations and cosmic bounce in a modified cosmological scenario
• The Semiclassical limit of $SU(3)$ Gauge Field Coherent States: Peakedness and Overlap Functions